Exit The slope between points A and B is . The slope between points B and C is . Antoine says all three of these points are on the same line. Which statement is true? A. Antoine is correct because both slopes are equal to . B. Antoine is incorrect because the slope of a line is always greater than 1. C. Antoine is incorrect because the slope is the same between any two points on a line. D. Antoine is correct because the slope is not the same between any two points on a line.

Complete Question:

The slope between A and B is ⅗.The slope between points B and C is 6/10. Antoine says all three of these points are on the same line. What statement is true?

A) Antoine is correct because both slopes are equal to ⅗.

B) Antoine is incorrect because the slope of a line is always greater than 1.

C) Antoine is incorrect because the slope is the same between any two points on a line.

D) Antoine is correct because the slope is not the same between any two points on a line

A) Antoine is correct because both slopes are equal to ⅗.

Step-by-step explanation:

We are given that:

Slope between A and B = ⅗

Slope between B and C = ⁶/10

If we reduce the fraction, ⁶/10 further, we would have: (2*3)/(2*5) = ³/5.

Therefore, slope between A and B, and slope between B and C would be the same = ⅗.

Since the slope are the same, it implies that all three points are in the same line.

Therefore, Antoine is correct.

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c